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We present a batch processing constant modulus algorithm (BP-CMA) derived by a nonlinear optimization approach to minimizing the constant modulus (CM) criterion. BP-CMA is a line search iteration algorithm. The search direction may be taken as deepest descent direction or Newton direction. The exact step size is obtained from the roots of a cubic equation. The initial value is calculated by using the eigenvectors of the signal subspace. The BP-CMA with the Newton direction has a fast convergence rate and can converge to the minima of the CM criterion after a few iterations.